A new polymorph of white phosphorus at ambient conditions

We present δ-P4, a new polymorph of white phosphorus. It crystallizes as a sixfold twin with the cell dimensions a = 18.302 (2), b = 18.302 (2), c = 36.441 (3) Å in the space group P212121 with 29 P4 tetrahedra in the asymmetric unit. Although their arrangement resembles the structure of α-Mn as proposed for α-P4, δ-P4 differs from α-P4.

The crystals, coated with a drop of inert oil, were transferred to the diffractometer at low temperature using the X-Temp2 device (Kottke & Stalke, 1993).The data were collected at 100 K with Mo Kα radiation on a Bruker SMART APEX II system based on D8 three-circle goniometers with Incoatec microfocus X-ray sources (IµS) and Incoatec QUAZAR mirror optics (Schulz et al., 2009).Data were collected for two crystals.For crystals 1 and 2, two or nine 0.5° omega scans were performed, respectively.

S2.2. Cell Determination
The automatic procedure in APEX (Bruker Nano Inc., 2021a) found a cubic cell with a = 36.5Å.
However, the diffraction pattern clearly indicated twinning.This can be interpreted as a three-fold twinning, and all reflections can be indexed with three different orientations and cell constants of approximately a = 18.3, b = 18.3, c = 36.5Å and  =  =  = 90 .

S2.3. Integration and Space Group Determination
The cell constants suggest a tetragonal space group.The integration was performed with SAINT (Bruker Nano Inc., 2021b) with three orientation matrices.TWINABS (Sevvana et al., 2019) was then used to detwin the data using Laue group 4/m.The fractional contributions of the three domains were determined to be 0.17, 0.45 and 0.38.The Rint was 0.1563 for all reflections of all domains.XPREP (Sheldrick, 2015c) could not find an acceptable space group consistent with the systematic absences.
The mean value for |E 2 -1| was 0.657, the low value being a warning sign of additional pseudomerohedral twinning (Herbst-Irmer, 2016).Therefore, TWINABS was repeated assuming Laue group mmm.Now the fractional contributions were determined to be 0.13, 0.47 and 0.40, while Rint improved to 0.086.Again the systematic absences were not quite clear but could be interpreted as consistent with space group P212121.twinning was taken into account and the integration was repeated, now with six orientation matrices (see Figure S1).TWINABS determined the fractional contributions to be 0.39, 0.35, 0.04, 0.08, 0.04, and 0.08, with a corresponding Rint of 0.1000.An Rint value of 0.516 for the tetragonal Laue group 4/m proved the tetragonal symmetry to be wrong.XPREP found the systematic absences for P212121 and |E 2 -1| was 0.714.

S2.4. Structure Solution and Refinement
The structure was solved in P212121 with SHELXD (Sheldrick, 2008); 116 phosphorous atoms in 29 P4 tetrahedra were found.The refinement with SHELXL (Sheldrick, 2015b) was then performed against the twinned data using only the reflections with contribution of the main component (Table S1).No disorder was observed.

S3. Structural Information
The 29 tetrahedra in the asymmetric unit are closely similar with P-P bond lengths in the range 2.138(5)-2.195(5)Å, with a mean value of 2.174 Å.The P-P-P bond angles lie in the range 59.03( 14

S4. Theoretical Investigation
For all calculations, version 6.3.1 of the Vienna ab initio simulation package (VASP) (Kresse & Furthmüller, 1996;Kresse & Joubert, 1999) was used.Gamma-centered k-point grids of size 15x5x11 for black phosphorus, 4x5x9 for red phosphorus, 5x5x2 for violet phosphorus, 5x6x9 for -P4, and 3x3x1 for -P4 were employed.The convergence criteria for the energies and the forces were set to 10 -6 eV and 1.5*10 -3 eV/Å, respectively.The crystal structures were fully relaxed with respect to the lattice parameters and atomic positions, starting from the experimental values, which were taken from the Inorganic Crystal Structure Database (ICSD) (Belsky et al., 2002) for the known allotropes and taken from experiments reported here for -IUCrJ (2024).11, https://doi.org/10.1107/S2052252523009247Supporting information, sup-6 the case of -P4, the primitive cell of the detwinned structure experimentally includes 116 P4 tetrahedra, resulting in a total of 464 atoms.
The analysis of the calculated lattice parameters given in Table S3 shows an increasing deviation from the experimental values over all the allotropes, with the largest change for -P4 when dispersion is taken into account.The overbinding tendency of PBE-D3/BJ is large for all systems investigated here.This can be explained partially by the size of the cell used for calculation, as can be seen from values given in Table S4, which show a strong variation of the lattice parameters with the size of the cell used because of the reduction of the symmetry.The resulting stacking along the a-axis is visualized in Figure S4.For the PBE calculations, the difference between a and b decreases from 0.0439 Å to 0.0265 Å.
Stacking along the c-axis (1x1x2) results in changes of the same magnitude.Taking dispersion into consideration, the effects are less pronounced but lead to an elongation of the lattice parameters.

S5. Hazards
White phosphorus is extremely pyrophoric when exposed to air.At all stages it should be handled under protective conditions, i.e. under water, argon or nitrogen gas.In addition, white phosphorus is toxic (LD50 (oral, rate): 3.0 mg/kg; maximum workplace concentration: 0.01 mg/m 3 ).Contaminated areas should immediately be treated with aqueous CuSO4-solutions to give the insoluble and non-bioavailable Cu3P2.
)-61.21(14)°, with a mean value of 60.0°.S3.1.Details of the Structure of -Mn compared to -P4 Mn1 occupies Wyckhoff position 2a (Type I) with 4 ̅ 3m symmetry, Mn2 position 8c (Type II) with 3m symmetry, Mn3 (Type III) and Mn4 (Type IV) position 24g with m symmetry.Mn1 is coordinated by 4 atoms of Type II and 12 of Type IV, Mn2 by one atom of Type I, 6 of Type III and 9 of Type IV, Mn3 by 2 atoms of Type II, 6 of Type III and 5 of Type IV, and Mn4 by one of Type I, 3 of Type II, 5 of Type III and 3 of Type IV.In the original paper (Oberteuffer & Ibers, 1970), there is a typing error in Table 5, where the coordination of Mn3 is described with one coordination to an atom of Type II and seven to Type III.However, the coordination with the distance of 2.930 Å is to Mn2 and not to Mn3.The same structural pattern holds for the P4 tetrahedra in -P4: One tetrahedron of Type I is surrounded by 4 tetrahedra of Type II and 12 of Type IV, 4 tetrahedra of Type II are surrounded by one tetrahedron of Type I, 6 of Type III and 9 of Type IV, 12 tetrahedra of Type III are surrounded by 2 tetrahedra of Type II, 6 of Type III and 5 of Type IV, and 12 tetrahedra of Type IV are surrounded by one of Type I, 3 of Type II, 5 of Type III and 3 of Type IV.

Figure S2
Figure S2 Stacking along the a-axis with red and blue spheres representing the primitive cells.The righthand panel shows the (2x1x1) supercell containing 928 P atoms.